COMPARATIVE
EFFICIENCY OF
SAMPLING PLANS
(I LLUSTRA TION - APPLE TREES)
rc ECONOMICS, STATISTICS, AND
COOPERATIVES SERVICE
u.s. DEPARTMENT
OF AGRICULTURE
COMPARATIVE EFFICIENCY OF SAMPLING PLANS
(ILLUSTRATION---APPLE
TREES)
By
Earl. E. Houseman
EconomicsJ Statistics
J and Cooperatives Service
U.S. Department of Agriculture
Septenber 1978
PREFACE
This publication
is regarded by the author as supple-
mentary training material for students who are familiar
with, or are studying, elementary theory of sampling includ-
ing stratification,
cluster sampling, ratio and regression
estimation, sampling with probability proportional
to size,
and multiple-stage
sampling.
After studying sampling methods
one at a time, it is important to get a unified view of the
several methods and the conditions under which they have
about the same or different variances.
In sampling various populations we quite often find two
or more techniques that are roughly equal in efficiency and
reduce sampling variance about as much as possible.
Admin-
istrative feasibility, costs, and freedom from potential
bias are important criteria for selecting a sampling plan
and become primary criteria when the choice ~s among plans
having small differences In sampling variance.
Ability to prejudge accurately the efficiency of alter-
native sample designs with reference to various survey
objectives and populations is important.
Such ability comes
from experience and detailed study of alternative techniques
of sampling a population and of making estimates.
Quite
often only two or three alternatives are compared in an
analysis because of limitations of data or only a few alter-
natives are of interest.
In this publication many alternative
I
sampling and estimation plans are applied to a small popula-
tion of apple trees and the results are recorded in tables
for comparative purposes.
The focus of attention is on the
magnitude of the differences in efficiency in relation to
the patterns of variation that exist.
For some readers, parts of the presentation
are proba